compressible flow modeling in star-ccm+ · pdf filetransonic flow over an airfoil the tutorial...

Copyright © 2011 CD-adapco. The following material constitutes a portion of the

CD-adapco training course entitled “Compressible Flow Analysis” and should not be

altered, edited or distributed without the consent of the author.

Compressible Flow Modeling in STAR-CCM+

Version 01/11




Content

2

Day 1

Compressible Flow

WORKSHOP: High-speed flow around a missile

WORKSHOP: Supersonic flow in a nozzle

WORKSHOP: Airfoil

3

27

73

97




Compressible Flow Modeling in STAR-CCM+

Version 01/11



altered, edited or distributed without the consent of the author. 4

Isentropic Compressible Flow Reference

where

A Area

m Mass flow rate

M Mach number

ℳ Molecular weight

P Static pressure

Pt Total pressure

R Specific gas constant

ℛ Universal gas constant [8314 J/kmol K]

T Static temperature

Tt Total temperature

V Velocity magnitude

g Ratio of specific heats

𝑇𝑡𝑇= 1 +

𝛾 − 1

2𝑀2

𝑃𝑡𝑃= 1 +

𝛾 − 1

2𝑀2

𝛾 𝛾−1

𝑉 = 𝑀 𝛾𝑅𝑇

𝑚

𝐴=

𝛾

𝑅

𝑃𝑡

𝑇𝑡𝑀 1 +

𝛾 − 1

2𝑀2

12−

𝛾𝛾−1

𝛾 =𝑐𝑝

𝑐𝑝 − 𝑅

𝑅 =ℛ

ℳ




Mesh / Grid Resolution

Vehicle / Blade surface resolution important

• At least 36 points around circle to obtain surface curvature resolution needed

• Aerodynamic surfaces (i.e. wings / winglets / blades) need to be resolved, especially at

leading and trailing edges, curvature resolution does help, but at least 6 cells across

trailing edge of surfaces needed

Wake and/or shock regions may need additional grid refinement – use volume

sources if needed in areas where flow is important but no geometrical features

exist on which to base furher grid refinement

Prism/extrusion layers can be crucial, especially in external aero type analysis




Domain Extent Considerations

External aerodynamic analyses

• Large enough domain aroung object / vehicle

• 10 spans width, 15-20 spans for wake region

All flows, recirculation at boundaries should be avoided, especially with shock

present




Free Stream Boundary

Typically used as ‚far field„ boundary conditions

for external aerodynamic problems

Specify the flow direction, Mach number, static

pressure, static temperature and turbulence

quantities

• Flow direction may be specified by Flow Angles

(see next slide), Components (in a specified

coordinate system) or as Boundary-Normal

(normal to the boundary surface)

7




8

Flow Angle Properties

Coordinate System The coordinate system to use.

Cartesian Specifies the Cartesian coordinate system.

Cylindrical Specifies the cylindrical coordinate system.

Laboratory Specifies the laboratory coordinate system.

Spherical Specifies the spherical coordinate system.

Rotation Convention The order in which to apply the rotations specified by the angles.

X Convention (Z-X-Z) For Euler angles (f, q, y), the first rotation is by angle f about the z-axis, the second is by angle q about the x-axis, and

the third is by angle y about the z-axis.

Y Convention (Z-Y-Z) For Euler angles (f, q, y), the first rotation is by angle f about the z-axis, the second is by angle q about the y-axis, and

the third is by angle y about the z-axis.

Yaw, Pitch, Roll Convention (Z-Y-X) For Euler angles (f, q, y ), the first rotation is by angle f about the z-axis, the second is by angle q about the y-axis,

and the third is by angle y about the x-axis.

Axes Convention How to treat the axes during rotations.

Fixed Axes Makes all rotations relative to the original fixed axes.

Moving Axes Makes second and third rotations relative to the rotated axes.

Reference Vector A unit vector that is rotated to convert angles and rotation conventions to a direction. Specified as a single three-part, comma-separated number.

Method Selects the method to use for specifying the angle data.

Constant Specifies the angle as a single three-part, comma-separated number. A Constant node will be added as a child to this

node. For two-dimensional cases, only your entries for the x- and y- directions will be relevant to the calculations

Field Function Defines the angle using a field function (typically user-defined). A Function node will be added as a child to this node

Table (iteration) Defines the angle as a function of iteration number. A Table (iteration) node will be added as a child to this node.

Table (time) Defines the angle as a function of physical time. A Table (time) node will be added as a child to this node.

Free Stream Boundary Flow Angles




Stagnation Inlet Boundary

Stagnation boundaries need special

consideration in supersonic flows. Pressure

ratio analysis needed to get correct inlet

conditions, i.e. Ptot / Pstat = f ( Mach )

Specify the Supersonic Static Pressure, Total

Pressure, Total Temperature and turbulent

quantities

• Note that both the total pressure and supersonic

pressure are relative to the specified reference

pressure

• The supersonic static pressure is designed to

establish incoming flow rate for a stagnation

boundary that is supersonic (otherwise it is

ignored)

• Be aware that if any time the boundary does go

supersonic (even prior to convergence), this value

will be used and the default or poor choice could

lead to divergence

9




Mass Flow Inlet Boundary

Most often used in conjunction with pressure

outlets

Specify the flow direction, mass flow rate,

supersonic static pressure, total temperature

and turbulence quantities

• Flow direction options are the same as for free

stream boundaries

• Supersonic static pressure is used only where the

inlet flow us supersonic (as with stagnation inlet

boundaries)

• Mass flow rate may be negative (outflow) despite

the name (see help for additional guidelines on this

option)

10




Pressure Outlet Boundary

Most often used in conjunction with stagnation

inlet and mass flow inlet boundaries

Specify the pressure, static temperature and

turbulence quantities

• For subsonic outflow, the specified pressure is

applied as a static pressure, while for supersonic

outflow the boundary pressure is extrapolated from

the cell adjacent to the boundary

• Where inflow occurs, the specified pressure is

applied as a total pressure

• Boundary velocities are extrapolated from the

interior in all cases

11




Initial Conditions

Specify (static) pressure, static temperature,

velocity and turbulence quantities

Intializing pressure:

• If there are no pressure boundaries, the specified

initial pressure must not result in a non-physical

absolute pressure

• For free-stream flows, the initial pressure should

equal the free-stream pressure

• For internal (duct) flows, the initial pressure should

be chosen so that it is equal to or higher than the

outlet pressure (helps to inhibit reversed flow at the

outlet)

It is a good idea to intialize the flow field prior to

running and judge if it makes sense

12




Solver Controls

The Coupled Implicit Solver is strongly recommended for all compressible flows

(especially if Mach number is greater than ~0.3)

For steady flows, the Courant Number is the key control parameter

• Default of 5.0 may be too high, especially for flows with shocks (lower this values to 1.0

or 2.0 and then ramp up over a few hundred iterations)

For transient flows the choice of the time step is crucial

• Set the time step such that the convective Courant number is ~1 everywhere

• Set stopping criteria based on residual tolerances of key variables (especially continuity,

momentum and temperature)

• Set sufficient number of inner iterations for all variables to converge (but not so many

that the solution is inefficient)




Coupled Flow Model

Advantages of the AUSM+ scheme

• Algorithmic simplicity and straightforward

extension for complex conservation laws

• Accurate capture of shock- and contact-

discontinuity

• Numerical solutions that preserve positivity and

satisfy entropy

• Reduced susceptibility to „carbuncle“ phenomena

AUSM+ recommmended for all compressible

flows

Explicit relaxation offers another way to relax

coupled flow solution (alternative to Courant

number)

• Change the Explicit Relaxation Factor from its

default value (1.0) to a lower value, e.g. 0.25

14




AMG Solver Controls

If instability persists, then modify

AMG Linear Solver settings

• Increase Convergence Tolerance to 0.1

(from default of 0.01)

• Increase V Cycle > Post-Sweeps to 3

(from default of 1)

• Decrease V Cycle > Max Levels to 2

(from default of 50)

15




Directional Mesh Reordering

Directional reordering may improve

solution convergence

• Reorder the mesh in the primary flow

direction

• Optimizes solver performance due to

the way it updates solution variables

• Also reduces the „bandwidth“of the

solution, making the solver more

efficient

• Right-click on Regions > [Regions

name] > Reorder Mesh

• In the popup window check the Use

directional reordering box and set the

direction vector as desired

16




Turbulence Modeling

General recommendations

• k-e are the models of choice for internal flows

• Spalart-Allmaras models are often the best choice for external flows with mild or no

separation

• k-w models are a good alternative to Spalart-Allmaras for external flows, especially

those with more severe separation

• Reynolds„ StressTransport models are recommended for flows with anisotropic

turbulence

The All-y+ wall treatment is recommended for any model for which it is available




Esitmation of Desired Near-Wall Cell Size

We generally wish to target a specific value of y+ for the near-wall mesh, where

𝑦+ =𝑢∗𝑦

𝜈 𝑢∗ =

𝜏𝑤𝜌

The wall sheat stress 𝜏𝑤 can be related to the skin friction coefficient:

𝐶𝑓 =𝜏𝑤

𝜌𝑈2

2

The skin friction coefficient can be estimated from correlations

• For a flat plate

• For pipe flow

𝐶𝑓

2=

0.036

𝑅𝑒𝐿1 5

𝐶𝑓

2=

0.039

𝑅𝑒𝐷1 5




Judging Convergence

For steady state, is solution unchanging?

• Do shock locations remain constant?

• Do vortices/separation points/recirculation zones remain unchanging over a number of

iterations?

• Constant temperature and pressure fields?

For transients, is each time step converging to the prescribed inner iterations

convergence criterion before reaching the maximum number of inner iterations?

Key data monitor settle to a constant value

• External aero lift/drag forces or Cl/Cd coefficients level off at a constant value

• Flow rates settle to constant values (such as in turbomachinery cases)

• Any other engineering quantities of note (swirl, forces, moments, etc.) are monitored

throughout and settle to constant values




Nozzle Best Practices

Set initial conditions to have pressure and temperature values as they would be

at Mach = 0.8

• This will help provide an initial velocity in the flow direction that is somewhat

representative and enables the flow to „wash“ over the geometry

• Without doing so, there is risk of low pressure „vacuum“ regions occuring which could

lead to instabilities

If convergence issues related to turbulence arise, try raising the turbulence

intensity to 0.1 and the turbulent viscosity ratio to 1000 for the initial and inflow

boundary conditions

At startup, a lot can happen and the vast gradients between a near laminar

startup and a turbulent flow early on could prove problematic for the solver

If the values for turbulence happen to be known at the boundaries, use these if

they are reasonable





KEY POINT: Ramp down exit pressure boundary conditions for temperature and

pressure using field functions





Results!

Note: The black and white d(rho)/d(P) result is obtained by

turning on temporary storage for the coupled solver settings)




Analysis Output/Post Processing

Contour Plots of

• Temperature

• Pressure

• Density

• Mach Number

• Velocity Magnitude

- All these help examine the physical nature of the flow and if there are shocks, are great properties

to visualize them!

- Can also help judge convergence of the flow fields

Velocity vector plots (to examine flow direction, swirl, wake, vortices, etc.)

Reports

• Lift/Drag monitors and plots for forces and coefficients are almost assuredly needed to

judge convergence and report results for external aero cases




Heat Transfer Coefficients & Adiabatic Wall Temperature

For external high-speed (compressible) flows, the appropriate choice of fluid

temperature is the „adiabatic wall temperature“

• An adjustment to the freestream temperature, it accounts for compressibility and viscous

dissipation effects

Adiabatic wall temperature is defined as:

𝑇𝑎𝑤 = 𝑇∞ 1 +1

2𝑟𝑐 𝛾 − 1 𝑀2

where 𝑇∞ is the freestream temperature, g is the specific heat ratio, M is the Mach number

and 𝑟𝑐 is the „recovery factor“

The recovery factor may be approximated by:

𝑟𝑐 ≈ 𝑃𝑟1 2 (laminar flow)

𝑟𝑐 ≈ 𝑃𝑟1 3 (turbulent flow)




WORKSHOP: High-speed flow around a

generic tactical missile

Version 01/11




Outline

Problem definition

• High-speed flow around a generic tactical missile (subsonic, transonic, supersonic)

• Various angles of attack may be simulated

Key features

• Polyhedral meshing with prismatic layers

• Freestream boundary condition used around the missile

Important boundary numbers

• Mach number: 1.5

• Angle of attack (AOA): 20 deg

• Static temperature: 293 K

• Static presure: 101325 Pa

• Feel free to change the above conditions as desired!




Data import

Load an existing simulation

• File > Load Simulation... or click on the

load icon in the System toolbar

• Browse to tacmissile_tutorial.sim

• Click Ok

29




Set Scene Parameters

Open the existing scene

• Right-click Scenes > Geometry Scene 1

> Open

Using the camera icon in the Vis

toolbar select

• Look Down > +X +Y +Z > Up +Y

Make scene transparent

• Click on the transparent icon in the

Vis toolbar

30




Save The Model

It„s a good idea to save the model every time you„ve accomplished a specific set

of tasks and you„re pretty sure that everything is okay with the model

• On the main menu, under File, choose save or simply click on the icon in the System

toolbar




Check Surface

Check the surface

• Right-click on Geometry > Parts

> tacmissile > Repair Surface...

• Click OK

In the new tab click on Start

Diagnostics, leave all defaults

and click OK

The check reveals that the

surface has 5 Pierced Faces,

1916 Poor Quality Faces and

16 Close Proximity Faces but

no other problems

We will use the Surface

Remesher to improve the

quality of the surface

32




Mesh Settings

Create a new mesh continuum and

fill it with the models

• Right-click on Continua > New > Mesh

Continuum

• Right-click on Continua > Mesh 1 >

Select Meshing Models...

We will create a polyhedral mesh

with prism layers

• Surface Remesher

• Polyhedral Mesher

• Prism Layer Mesher

33




Mesh Reference Values

Set the reference values, these will be the default

mesh parameters used on all boundaries

• Right-click on Mesh 1 > Reference Values > Edit...

Tet/Poly Density controls the overall volume mesh

density, while the Growth Factor controls the rate of

growth from fine to coarse areas

Tet/Poly Volume Blending controls the rate of cell

growth from volume sources

34

Reference Values Value

Base Size 0.2 m

Prism Layer Thickness Relative 2%

Surface Size: Relative Minimum Size

Relative Target Size

2%

20%

Tet/Poly Density Density

Growth Factor

0.6

1.4

Tet/Poly Volume

Blending

Blending Factor 0.8




Boundary Mesh Values

We will change the default mesh settings at

several boundaries:

The leading edges of the fins requires a

much finer mesh than the rest of the

domain

• Right-click on Regions > Body 1 > Boundaries

> fin LE > Edit...

• Set the values according to the table

Repeat this for fin TE

35

Mesh Conditions fin LE fin TE

Custom Surface Size Yes Yes

Mesh Values

Surface Size: Relative Minimum Size 0.05% 0.5%

Surface Size: Relative Target Size 0.4% 1%





The mesh on the symmetry boundary

needs to be able to grow from a small

size near the missule surface to a

much larger size further away

• Right-click on Regions > Body 1 >

Boundaries > symmetry > Edit...

• Change the boundary type

Boundary Type: Symmetry


36

Mesh Conditions symmetry

Custom Surface Size Yes

Mesh Values

Surface Size: Relative Minimum Size 1%

Surface Size: Relative Target Size 2000%





The freestream boundary is the

hemisphere sourrounding the one side of

the missile

The mesh here is large, so the Minimum

Surface Size is left at its default while the

Target Surface Size is set to a large value

• Right-click on Regions > Body 1 > Boundaries

> freestream > Edit...

• Change the boundary type

Boundary Type: Free Stream


37

Mesh Conditions freestream

Custom Surface Size Yes

Mesh Values

Surface Size: Relative Minimum Size 25%

Surface Size: Relative Target Size 2000%




Volume Mesh Refinement

STAR-CCM+ has the ability to locally

refine the mesh in the region

sourrounded by a volume

• We will do this around the missile

Create the volume

• Right-click on Geometry > Parts > New

Shape Part > Cylinder

• Click Create

38

Start End

X 0 m 0 m

Y 0 m 0 m

Z -0.0224 m 0.1047 m

Radius 0.1 m




Volume Mesh Refinement

Create a volumetric control with the

cylinder as volume source

• Right-click Contina > Mesh 1 >

Volumetric Control > New

• Right-click Volumetric Control 1 > Edit...

Use the newly created cylinder as

input part

Part Group: Cylinder


39

Mesh Conditions freestream

Polyhedral Mesher: Customize Yes

Surface Remesher: Customize Yes

Mesh Values

Custom Size: Relative Size 6%




Physics Settings

Create a new physics continuum and fill it

with the models

• Right-click on Continua > New > Physics

Continuum

• Right-click on Continua > Physics 1 > Select

Models...

For high-speed compressible flow the

coupled solvers are best

We expect significant flow separation at this

large angle of attack, so the SST (Menter)

K-Omega model with All y+ Wall Treatment

is chosen

• Three Dimensional

• Steady

• Gas

• Coupled Flow

40

• Turbulent

• K-Omega Turbulence




Solver Settings

The AUSM+ FVS scheme is chosen

for the coupled solver

• Physics 1 > Models > Coupled Flow

• Set AUSM+ FVS in the properties

window as the scheme for Coupled

Inviscid Flux

41




Air Material Properties

Deceleration of the flow near the

missile surface will create large static

temperature gradients, so

Sutherland‘s Law is used for

Dynamic Viscosity and Thermal

Conductivity

• Right-click Physics 1 > Models > Air >

Material Properties > Edit...

• Choose Sutherland‘s Law, leave the

default values

Other properties have a weaker

temperature dependence and are left

constant

42




Air Reference Values

All reference values will stay

unchanged

• The reference pressure is set to the

static ambient pressure: 101325 Pa

43




Air Initial Conditions

The static pressure is relative to the

reference pressure, so it is set to

zero

The static temperature is set to the

ambient temperature

The velocity components correspond

to the specified Mach number,

ambient temperature and angle of

attack

• Right-click on Continua > Physics 1 >

Initial Conditions > Edit...

44

Initial Parameter Value

Velocity Components [0.0, 176.06, 483.72] m/s




Boundary Condition: Free Stream

The physics conditions for the

freestream boundary needs to be

changed

• Right-click Regions > Body 1 >

Boundaries > freestream > Edit...

45

Physics Conditions freestream

Flow Direction Specification Angles

Physics Values

Flow Angles: Reference Vector [0.0, 0.0, 1.0]

Flow Angles: Constant [0.0, -20.0, 0.0] deg]

Mach Number: Constant 1.5




Boundary Conditions

The symmetry boundary is already if type Symmetry Plane

• No other settings are needed for this type of boundary

All other boundaries are adiabatic, no-slip walls which is the default type Wall

Summary of boundary types Boundary Name Boundary Type

freestream Free Stream

symmetry Symmetry Plane

aft

Wall

base

body mid

fin LE

fin sides

fin TE

nose

scoop




Mesh Generation

We are now ready to generate the mesh!!!

We will generate the surface mesh and the volume mesh in two separate steps

• Generate the surface mesh

• See that is it generated successfully (no errors)

• Visually inspect it to see if density is as desired

• Only after these steps are complete should volume mesh generation be attempted

Generate the surface mesh now – this can be done in one of two ways

• On the main menu, select Mesh > Generate Surface Mesh

• Click the Generate Surface Mesh icon on the Mesh Generation toolbar

Generate Surface Mesh

Generate Volume Mesh




Surface Mesh

To view the remeshed

surface, create a new

mesh scene

• Click on the scene icon

in the Vis toolbar

The mesh is coarse

but acceptable for our

purposes

• Accurate results would

require a muchfiner

mesh

48




Volume Mesh

Now generate the volume

mesh – again in one of two

ways

• On the main menu, select Mesh

> Generate Volume Mesh

• Click the Generate Volume

Mesh icon on the Mesh

Generation toolbar

To view the volume

mesh create a new

mesh scene

49




Volume Mesh Section

Create a cut through the geometry

• Change the view using the camera icon

in the Vis toolbar and select Look Down

> +X > Up +Y

• Click on the Create Plane Section icon

and create the section as shown

• Choose to create a New Geometry

Displayer

In the scene/plot tab disable Mesh 1

displayer

• Right-click Mesh Scene 2 > Displayers

> Mesh 1 > Toggle Visibility

50




Volume Mesh Section

Turn the mesh display on clicking on

the globe icon in the Vis toolbar

Note that there are two prism layers

adjacent to the wall boundaries

forming the surface of the missile

Note also that there are no prism

layers adjacent to the symmetry and

freestream boundaries

Once again the mesh is too coarse

for accurate results, but acceptable

for our purposes

51




Solver Settings

Right-click on Solvers > Coupled

Implicit and choose Edit…

To accelerate the convergence,

increase the Courant Number to 10.0

All other settings can be left at their

defaults

52




Stopping Criterion

Click on Stopping Criteria >

Maximum Steps and set the

Maximum Steps to 200

53




Post Processing: Frontal Area

Create a report to calculate the

frontal area of the surface

• Right-click Reports > New Report >

Frontal Area

• Rename this report frontal area

• Right-click frontal area > Edit…

The defaults for View Up, Normal and

Units are acceptable

For Parts, select all parts that

comprise the missile surface

• Do not select Body 1: freestream or

Body1: symmetry

54




Post Processing: Frontal Area

Right-click Reports > frontal area and select Run Report

The Output window should appear as follows (the exact value of area depends

on the created mesh)




Post Processing: Drag Coefficient Report

Create a Force Coefficient Report

• Right-click Reports > New Report >

Force Coefficient

• Rename this report cd

• Set the Reference Density, Reference

Velocity and Reference Area as shown

• Note that the computed frontal area has

been used as the Reference Area

• Select Pressure + Shear as the Force

Option

• The Direction is set to be aligned with

the flow direction

• Select only the Parts that comprise the

missile surface (same as for the frontal

area)

56




Post Processing: Lift Coefficient Report

Create a lift coefficient report

The only difference here is the

direction of the force, so we will

simply copy and paste the cd report

and change the direction vector

• Rename the report to cl

57




Post-Processing: Drag & Lift Coefficient Plots

We must now create monitors and

plots from these reports

• Click on Reports > cd, hold down the

Ctrl key, and click on Reports > cl

While continuing to hold down the

Ctrl key, right click on either report

name and choose Create Monitor

and Plot from Report

In the Create Plot from Reports…

window, select Multiple Plots (one

per report)

58




Post-Processing: Velocity Vector Scene

Create a new vector scene

• Rename it to Velocity Vectors

• Change the view

- Look Down > +X+Y+Z > Up +Y

Go to the scene/tab panel

• Select Regions > Body 1 > symmetry

to be put in Parts

Click on Displayers > Vector 1 and

change the Vector Scale to Screen

Size in the Properties window

59




Post-Processing: Streamline/Mach Number Scene

We now compose a scene with several displayers, starting with an empty scene

1. Displayer: Scalar displayer showing Mach number on the missile surface

2. Displayer: Streamline displayer

3. Displayer: Geometry displayer showing the mesh on the missile surface




Post-Processing: Streamline/Mach Number Scene

Create an empty scene

• Rename to Mach Number with Streamlines

• Change the view to Look Down > -X > Up +Y

• We will use a Symmetry Transform for all

displayers, this was automatically created by

STAR-CCM+ using the definition of the

symmetry boundary

61




Post-Processing: Streamlines

Define new streamlines and add them to a new

displayer in the scene

• Right-click Derived Parts > New Part > Streamline…

• Change the Seed Mode to Line Seed

• Set the starting and ending points for the line seed as

shown, as well as the resolution

• In the Display sub-window, select New Streamline

Displayer

• Click Create

Rename this derived part to streamline

62

Start End

X 0 m -0.04 m

Y -0.9 m -0.09 m

Z -1.5 m -1.5 m

Resolution 40




Post-Processing: Streamline Displayer

In the Scene Explorer of the Mach Number with Streamlines scene, make the

following settings for the streamline displayer:

• Scalar Field: Pressure Coefficient

• Color Bar: invisible

• Transform: symmetry 1




Post-Processing: Scalar Displayer

Create a new scalar displayer

• Right-click Displayers > New > Scalar

• For Parts, select only the parts that


• As Scalar Field function choose Mach

Number

• Click on the Scalar 1 displayer and in the

properties window change the Contour

Style to Smooth Filled

• Set Transform to symmetry 1

64




Post-Processing: Geometry Displayer

Create a new scalar displayer

• Right-click Displayers > New > Geometry

• For Parts, select only the parts that


• Click on the Geometry 1 displayer and in

the properties window check the Mesh

box, uncheck the Outline box

• Set Transform to symmetry 1

65




Run Simulation

It‟s now time to run the analysis!!!

This can be done in either of two ways:

• On the main menu, select Solution > Run

• Click the Run button on the Solution toolbar




Residuals Plot




Drag Coefficient Plot




Lift Coefficient Plot




Velocity Vectors Scene




Mach Number with Streamlines Scene




Summary

An analysis of high-speed compressible flow around a missile at 20° AOA has

been performed

A polyhedral mesh with prism layers and local refinement around the fin leading

and trailing edges has been constructed

• It was noted that production analyses should use a much finer mesh than what was

used here

The analysis and post-processing setup was performed




WORKSHOP: Supersonic Flow in a

Converging-Diverging Nozzle

Version 01/11




Outline

Problem definition

• Steady 2D flow in a converging-diverging nozzle with shocks

Key features

• Polyhedral meshing with prismatic layers

• Stagnation inlet and pressure outlet boundaries

• Coupled implicit solver

• Boundary condition ramping using field functions




Data import

Start a new STAR-CCM+ session

• File > New Simulation... or click on the

new icon in the System toolbar

• Click OK

Import the mesh

• File > Import > Import Volume Mesh...

• Navigate to the workshop 2 folder, then

seelct nozzle.ccm

• Click OK

75




Imported Mesh

The imported mesh is 2D and

consists of approximately

197K polyhedral cells

As seen in the screenshot

below, there are 3 prism layers

adjacent to the duct walls

76




Physics Settings

Fill the existing physics continuum with models

• Right-click on Continua > Physics 1 > Select

Models...

Note in particular the choice of the

Axisymmetric, Ideal Gas and Coupled solver

models for this analysis (you may need to disable

Two Dimensional)

• Axisymmetric

• Steady

• Gas

• Coupled Flow

• Ideal Gas

• Turbulent

• K-Epsilon Turbulence

77




Solver Settings

Change the settings of the coupled

flow solver in its properties window

• Continua > Physics 1 > Coupled Flow

- Explicit relaxation: 0.25

- Coupled Inciscid Flux: AUSM+ FVS

78




Boundary Condition: Axis

Check that the boundary type for axis

boundaries is set to Axis

• With the Ctrl key pressed, select

Regions > Body_1_2D > Boundaries >

far field axis and nozzle axis and check

in the Properties window that Type is

set to Axis

• The icons in front of the boundaries are

also good indicators for the type of the

boundary

• Summary of boundary types:

79

Boundary Name Boundary Type

pressure outlet Pressure

stagnation inlet Stagnation Inlet

far field axis Axis

nozzle axis

near nozzle vertical wall No-slip Wall

nozzle wall

top slip wall Slip Wall




Boundary Condition: Wall

Ensure that the Shear Stress

Specification for top slip wall is Slip

• Regions > Body_1_2D > Boundaries >

top slip wall > Physcis Conditions >

Shear Stress Specification: Slip

80




Boundary Condition: Stagnation Inlet

The physics conditions for the inlet

boundary needs to be changed

• Right-click Regions > Body 1 >

Boundaries > stagnation inlet > Edit...

• Check that Type is Stagnation Inlet

• Set values according to the table:

Note: Since the inflow is expected

to be subsonic, the Supersonic

Static Pressure value should not

affect the final solution

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Physics Conditions stagnation inlet

Supersonic Static Pressure 9E+05 Pa

Total Pressure 1E+06 Pa

Total Temperature 2300 K

Turbulence Intensity 0.1

Turbulent Viscosity Ratio 1E+04




Boundary Conditions: Ramping Functions

Recall that a helpful strategy for starting up

nozzle problems is to ramp the outlet conditions

down from the inlet conditions

• To do this we will use field functions

To define a field function, right-click Tools >

Field Functions > New

• This creates a field function named User Field

Function 1

We will create two new field functions, one for

the pressure, one for the temperature

• Relative Pressure shall be ramped from 1E+06 Pa

to zero over 1000 iterations

• Temperature is ramped from 2300 K to 300 K over

1000 iterations

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Boundary Conditions: Ramping Functions

Name Function Name Dimensions Definition

P_Down pdown Pressure ($Iteration < 1000) ? 1e6*(1-$Iteration/1000) : 0.0

T_down tdown Temperature ($Iteration < 1000) ? (300 + 2000*(1-$Iteration/1000)) : 300




Boundary Conditions: Pressure Outlet

Set the field functions P_down and

T_down as boundary condition for

pressure outlet

• Right-click Regions > Body_1_2D >

Boundaries > pressure outlet > Edit...

• Check that Type is Pressure Outlet

• Set values according to the table:

84

Physics Conditions pressure outlet

Pressure: Method Field Function

Pressure: Field Function P_down

Temperature: Method Field Function

Temperature: Field Function T_down






Physics: Initial Conditions

The values set as initial conditions are basically

the same as the conditions of the stagnation inlet

• The velocity is simply an estimate of the average

velocity in the domain

• Pressure is set to a value that results in Ma=0.8 in the

smallest part (Pt = 106 Pa)

85

Initial Conditions

Pressure 6.5445E+05 Pa

Temperature 2300 K


Turbulent Velocity Scale 100 m/s


Velocity [0.0, 0.0, 0.0]

𝑃 = 𝑃𝑡

1 + 𝛾−12 𝑀2

𝛾𝛾−1




Solver Parameters and Stopping Criterium

We will decrease the Courant

Number in the coupled solver

• Click on Solvers > Coupled Implicit and

set the Courant Number value to 2.0

• This will help to stabilize the

convergence, especially in the early

stages

• We will leave the Courant Number at

2.0 for the entire analysis, but we could

have also ramped it from 2.0 to some

higher value

Set the Stopping Criteria > Maximum

Steps value to 8000

86




Post Processing: Transform

We will define a transform so that we

can view a serction through the full

3D axisymmetric geometry

• Right-click Tools > Transforms > New

Graphics Transform > Simple

Transform

- This creates a new transform named

Simple Transform 1

• Set the Rotation Angle and Rotation

Axis

87

Transform Properties

Rotation Angle 180 deg

Rotation Axis [1, 0, 0]




Post Processing: Mach Number Scene

We now compose a scene with two scalar displayers

1. Displayer: Scalar displayer showing Mach number

2. Displayer: Scalar displayer, same settings plus Transform





Create a new scalar scene

• Rename to Mach Number

• Note that the region is already added to

Parts

Click on the scene/plot tab

Make the outline displayer invisible

• Right-click Displayers > Outline 1 >

Toggle Visibility

Settings for Displayer > Scalar 1

• For Contour Style select Smooth Filled

• As Scalar Field choose Mach Number

89





Copy the Scalar 1 displayer

• This creates a new displayer named Copy of Scalar 1

Settings for Displayer > Copy of Scalar 1

• Change Transform to Simple Transform 1

• Uncheck the Visible box under Color Bar

90




Run Simulation

Create other scenes as desired (e.g. for pressure, temperature, velocity vectors)

Now run the simulation in either of two ways:

• On the main menu, select Solution > Run

• Click the Run button on the Solution toolbar

Note: The simulation will run for 8000 iterations for about 3 hours on 4 processors.

To get the following pictures it is necessary to run the simulation much longer.

Increase the Courant number to 5.0 after the first 8000 steps and run it as long as

necessary (approx. 30,000 iterations).




Mach Number

30,000 iterations

92

8,000 iterations

16,000 iterations




Absolute Pressure

30,000 iterations

93

8,000 iterations

16,000 iterations




Temperature

30,000 iterations

94

8,000 iterations

16,000 iterations




Summary

The flow is fairly well-developed and we can see the shock at the nozzle throat

and the beginning of the formation of shock diamonds downstream of the nozzle

It was necessary to reduce the Courant Number for the coupled implicit solver to

2.0 (from the default value of 5.0) to start the solution, but it can probably be

increased now that the important flow features are in place

Field functions were used to ramp down the outlet conditions – this is a useful

approach for many high-speed compressible internal flow problems

Copyright © 2011 CD-adapco

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Visit https://support.cd-adapco.com to find this material under Past Courses

• Please fill in our online training feedback form that is located there too

STAR-CCM+ User Guide 7361

Version 6.06.015

Transonic Flow over an AirfoilThe tutorial simulates two-dimensional, turbulent, compressible, transonic air flow over an idealized airfoil, as shown below. The free-stream Mach number is 0.725 and the angle of attack is 2.54o. This corresponds to RAE2822 case 6 in Reference [272].

The free-stream flow is subsonic, becoming supersonic on the suction side of the airfoil and subsonic again through a shock wave. The lift and drag coefficients are monitored to help determine whether convergence is reached. The final distribution of the pressure coefficient on the airfoil is then compared to experimental data.

Importing the Mesh and Naming the Simulation

Start up STAR-CCM+ and select the New Simulation option from the menu bar.

Continue by importing the mesh and naming the simulation. A one-cell-thick, three-dimensional, hexahedral mesh has been prepared for this analysis. The mesh corresponds to an angle of attack of 0o in the default Laboratory coordinate system.• Select File > Import > Import Volume Mesh... from the menus.• In the Open dialog, simply navigate to the doc/tutorials/aerofoil

subdirectory of your STAR-CCM+ installation directory and select file aerofoil.ccm which contains the mesh and boundary definitions.

• Click the Open button to start the import.

STAR-CCM+ will provide feedback on the import process, which will take a few seconds, in the Output window. A geometry scene will be created in the Graphics window.

Finally, save the new simulation to disk under file name aerofoil.sim.

STAR-CCM+ User Guide Transonic Flow over an Airfoil 7362

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Converting to a Two-Dimensional Mesh

The mesh region can now be converted to a two-dimensional one. There are special requirements in STAR-CCM+ for three-dimensional meshes that need to be converted to two-dimensional. These are: • The grid must be aligned with the X-Y plane.• The grid must have a boundary plane at the Z = 0 location.

The mesh imported for this tutorial was built with these requirements in mind. Were the grid not to conform to the above conditions, it would have been necessary to realign the region using transformation and rotation facilities available in STAR-CCM+.• Select Mesh > Convert to 2D...

• In the Convert Regions to 2D dialog that appears, make sure the checkbox of the Delete 3D regions after conversion option is ticked, and click OK.

Once you have clicked OK, the mesh conversion will take place and the Geometry Scene 1 display will show the two-dimensional geometry in the


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Graphics window. (If the image does not appear immediately, simply click the (Reset View) button on the toolbar.)

All the geometry parts will be shown, viewed from the +z-direction. The mouse rotation option is suppressed for two-dimensional scenes.• Right-click the Physics 1 continuum node and select Delete.• Click Yes in the confirmation dialog.

Setting up the Models

Models define the spatial and temporal solution methods and the physical properties of the flow. In this example, the flow is steady, turbulent and compressible. The default Spalart-Allmaras turbulence model and the ideal gas model will be used. The analysis will also use the coupled solver, which is recommended for all supersonic and transonic compressible flows.

By default, a continuum called Physics 1 2D is created when the mesh is converted to two-dimensional. To use a more appropriate name:• Right-click the Physics 1 2D node and select Rename...Change the name

to Aerofoil.


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The continuum definition will now be edited to select appropriate physical models for the fluid.• Right-click the Aerofoil continuum node and select item Select models.

The Physics Model Selection dialog will guide you through the model selection process by showing only options that are appropriate to the choices already made.• Make sure that the Two Dimensional radio button is selected from the

Space group box.• Select Gas in the Material group box.• Select Coupled Flow in the Flow group box.• Select Ideal Gas in the Equation of State group box.• Select Steady in the Time group box.• Select Turbulent in the Viscous Regime group box.• Select Spalart-Allmaras Turbulence in the Reynolds-Averaged Turbulence

group box.• Click Close.

Inside the Continua node, the color of the Aerofoil node has turned from gray to blue to indicate that models have been activated.• Open the Aerofoil node and then the Models node.


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The selected models now appear within that node.

• Save the simulation .

Setting Material Properties• Open the Gas and Air nodes.

The material properties for air are contained within.• Select the Material Properties > Dynamic Viscosity > Constant node.• In the Properties window, change the dynamic viscosity value to

4.61e-5 PaS. This corresponds to a Reynolds number of 6.5 x 106 [272].


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Setting Initial Conditions

The initial velocity field will apply free-stream conditions across the entire domain, i.e. a velocity of 247.967 m/s calculated using the equation:

(1641)

where , , and

To specify an angle of attack of 2.54o for the initial velocity, we will create a new coordinate system.• Open the Tools node at the bottom of the simulation tree and right-click

the Coordinate Systems > Laboratory > Local Coordinate Systems node.• Select New > Cartesian.

u M�Pref�ref------------=

M 0.725= Pref 101325= �ref 1.2126= � 1.4=


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An in-place dialog will appear to help you create the coordinate system.

• In the Axis Definition group box, change the i Direction to the following:[0.999, 0.0443, 0]

• Click Renormalize. The j Direction will change automatically to ensure that the axes are perpendicular. The i Direction may also readjust itself


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slightly.• Click Create, then Close.

A node called Cartesian 1 will be created within the Coordinate Systems node. The resulting Properties window is shown below.

This now defines a coordinate system that, when viewed down the +z-axis, has its x- and y-axes rotated anti-clockwise through an angle of 2.54o compared to the laboratory system.• Return to the Aerofoil continuum node and select the Initial Conditions >

Velocity node.

• In the Properties window, change the Coordinate System property to Laboratory -> Cartesian 1.

• Select the Velocity > Constant node.• In the Properties window, change the Value to

[247.967, 0.0, 0.0] m/s.

To specify the initial temperature:• Select the Static Temperature > Constant node.


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• In the Properties window change the Value to 291 K.

The default values for the remaining initial conditions are suitable for this problem.

Save the simulation.

Setting Boundary Conditions and Values

The geometry used for this tutorial has only two boundaries:• A wall boundary representing the surface of the airfoil.• A free-stream boundary at the external edge of the solution domain.

• Open the Regions node, then right-click the Default_Fluid 2D node and select Rename....

• Enter the name Fluid and click OK.• Select the Fluid > Boundaries > freestream > Physics Conditions > Flow

Direction Specification node.

• In the Properties window, make sure that the Method property is set to Components.


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• Select the Physics Values > Flow Direction node.

• As for the initial velocity, change the Coordinate System property to Laboratory -> Cartesian 1.

• Select the Mach Number > Constant node.


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• Change the Value property to 0.725.• Select the Static Temperature > Constant node.• Change the Value property to 291 K.

All other conditions for the free-stream boundary and the default wall boundary conditions are suitable for this problem.

Save the simulation .

Setting Solver Parameters

The simplicity of this problem allows a rapidly converging solution to be attained using a large Courant number. In problems involving more complex geometries or physics, attempting to shorten the run time in this way may cause the run to diverge. To increase the Courant number:• Select the Solvers > Coupled Implicit node.

• In the Properties window, change the Courant Number to 20.0.

Save the simulation.


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Visualizing and Initializing the Solution

We will view the Mach number profile during the run to monitor the supersonic flow region above the airfoil.

Start by creating a new scalar scene.• Right-click on the Scenes node, and select New Scene > Scalar.

The Scalar Scene 1 display will appear.• Right-click on the scalar bar at the bottom of the display and select Mach

Number > Lab Reference Frame from the pop-up menu.

• Initialize the run by clicking the Initialize Solution button in the toolbar, then use the middle mouse button to zoom in on the airfoil in the center


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of the scalar scene.

To change the style of the Mach number contours:• Select the Scalar Scene 1 > Displayers > Scalar 1 node.• In the Properties window, change the Contour Style property to Smooth

Filled.

Save the simulation .

Plotting Graphs

The lift and drag coefficients will be plotted to help in determining when the analysis has converged.


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• Right-click the Reports node and select New Report > Force Coefficient.

A new report node named Force Coefficient 1 will be created.• Rename this node Drag Coefficient then enter the information

shown below in the Properties window.

• Right-click the Drag Coefficient node and select Create Monitor and Plot from Report.

A new plot node will appear named Drag Coefficient Monitor Plot.


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• Double-click on the Drag Coefficient Monitor Plot node to display the empty plot in the Graphics window.

• Repeat the steps described above to create and display a plot for the lift coefficient. All settings should be the same as for the drag coefficient except that the report node should be renamed Lift Coefficient and its Direction property should be set to [-0.0443, 0.9990, 0.0].

Experimental data for the pressure coefficient on the airfoil are provided in file aero_exp.xy in the doc/tutorials/aerofoil directory. These will be plotted on a graph alongside the results of the analysis.

To plot the experimental data:• Right-click the Tools > Tables node and then select New Table > File....• Locate and open file aero_exp.xy• Right-click the Plots node and select New Plot > X-Y.

• Open the XY Plot 1 node, then right-click the Tabular node and select


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New Tabular Data Set.

A new node named tabular will appear within the Tabular node.• In the Properties window, select aero_exp for the Table property.

Make sure that the X Column and Y Column properties are filled as shown below.

A graph of the experimental data will appear in XY Plot 1.

To add the numerical data to the same graph:• Select the XY Plot 1 node.• In the Properties window, click on the Parts property and select Fluid: wall

in the Select Objects dialog.


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• Select the Y Types > Y Type 1 > Scalar node.

• In the Properties window, select Pressure Coefficient for the Scalar property.

The initial pressure coefficient is shown in the XY Plot 1 as being zero everywhere.

The pressure coefficient requires specification of a reference pressure and a reference velocity.• Select the Tools > Field Functions > Pressure Coefficient node.• In the Properties window, enter a Reference Density of 1.2126 kg/m3

and a Reference Velocity of 247.967 m/s, as shown in the following screenshot.


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The usual convention in aerodynamics problems is to reverse the y-axis orientation in pressure coefficient plots.• Select the XY Plot 1 > Axes node.

• Click on the Axis Orientation property and select the option shown below.

The setup is now complete. • Save the simulation .


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Running the Simulation• To run the simulation, click the (Run) button in the top toolbar. If you

do not see this button, use the Solution > Run menu item.

The Residuals display will be created automatically and will show the progress being made by the solver. You may observe the run progress by selecting one of the tabs at the top of the Graphics window. The Scalar Scene 1 display after about 50 iterations is shown below.

During the run, it is possible to stop the analysis by clicking the (Stop) button in the toolbar. If you do halt the simulation, it can be continued again later by clicking the (Run) button. If left alone, the simulation will continue until 1000 iterations have been completed.

Once this stage is reached, check that the solution has converged by examining the lift and drag coefficient plots.• Select the Plots > Lift Coefficient Monitor Plot > Axes > Y Axis > Labels node.• In the Properties window, change the Minimum and Maximum properties

to 0.2 and 0.8, respectively, to zoom in on the relevant part of the graph.


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• Double-click the Lift Coefficient Monitor Plot node to display the results in the Graphics window.


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• Similarly, display the drag coefficient plot and adjust its y-axis scale.

Both monitors have reached constant values so it is reasonable to conclude that the solution has converged.• Save the simulation .


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Visualizing the Results

The Scalar Scene 1 display shows the Mach number profile at the end of the run. The profile shows the transonic flow around the airfoil, including the shock wave produced above it.


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Validating the Results

A graph showing the comparison between numerical and experimental data can be viewed by selecting the XY Plot 1 tab, as shown below with the X axis scale adjusted.

Other than the shock position, which is in error as a result of the mesh coarseness and choice of turbulence model, the numerical pressure coefficients compare well with the experimental data. The lift coefficient determined experimentally for this case is 0.743 [272]. To see the value calculated by STAR-CCM+:


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• Right-click the Reports > Lift Coefficient node and then select Run Report.

In the Output window, a tab named Lift Coefficient Report will display the relevant report and show a lift coefficient of 0.732, which is within 2% of the experimental value. Similarly, the drag coefficient report will give a value of 0.0137, which also compares well to the experimental value of 0.0127.

Summary

This STAR-CCM+ tutorial introduced the following features:• Defining models for compressible flow problems.• Defining the material properties required for the selected models.• Setting solver parameters for a steady-state run.• Plotting graphs comparing results with experimental data.• Initializing and running the solver to a specified stopping criterion.• Analyzing the results using the built-in visualization facilities.

Airfoil Tutorial Bibliography[272] Cook, P.H., M.A. McDonald, M.C.P. Firmin “Aerofoil RAE 2822 -

Pressure Distributions, and Boundary Layer and Wake Measurements Experimental Data Base for Computer Program Assessment”, AGARD Report AR 138, 1979

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